lie groups - Lie Algebra of SO (n) - Mathematics Stack Exchange
Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. Physicists prefer to use hermitian operators, while mathematicians are not biased towards …
Fundamental group of the special orthogonal group SO(n)
Also, if I'm not mistaken, Steenrod gives a more direct argument in "Topology of Fibre Bundles," but he might be using the long exact sequence of a fibration (which you mentioned).
Homotopy groups O(N) and SO(N): $\\pi_m(O(N))$ v.s.
Oct 3, 2017 · I have known the data of $\\pi_m(SO(N))$ from this Table: $$\\overset{\\displaystyle\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\textbf{Homotopy …
Prove that the manifold $SO (n)$ is connected
The question really is that simple: Prove that the manifold $SO (n) \subset GL (n, \mathbb {R})$ is connected. it is very easy to see that the elements of $SO (n ...
Dimension of SO (n) and its generators - Mathematics Stack …
Nov 18, 2015 · The generators of $SO(n)$ are pure imaginary antisymmetric $n \\times n$ matrices. How can this fact be used to show that the dimension of $SO(n)$ is $\\frac{n(n-1 ...
Why $\\operatorname{Spin}(n)$ is the double cover of $SO(n)$?
Dec 16, 2024 · Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges,
Age problem of father and son - Mathematics Stack Exchange
A father's age is now five times that of his first born son. Six year from now, the old man's age will be only three times that his first born son. Find age of each.
Lie Algebra of U(N) and SO(N) - Mathematics Stack Exchange
Oct 8, 2012 · U (N) and SO (N) are quite important groups in physics. I thought I would find this with an easy google search. Apparently NOT! What is the Lie algebra and Lie bracket of the …
semi-simple and simple lie group,SO (n) for n even
Mar 23, 2021 · It is stated in the literature that SO(n) for n even is semi-simple or simple and either one of these means that it has no non-identity abelian factor groups but I,-I is an order 2 …
orthogonal matrices - Irreducible representations of $SO (N ...
Sep 21, 2020 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation …